Optimize attempts in a timed logic test
Quick Overview
This question evaluates a candidate's understanding of expected value, time-constrained optimization, efficiency metrics (score per second), and discrete decision-making under uncertainty when allocating time across heterogeneous items.
Shopify
Oct 13, 2025, 9:49 PM
Data Scientist
HR Screen
Statistics & Math
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Timed OA: Maximize Expected Score Under a Time Limit
Context: You have 25 minutes (1,500 seconds) to attempt up to 30 multiple-choice items. You may choose which items to attempt; once you skip a question, you cannot return. Scoring is +3 for a correct answer, 0 for blank, and −1 for a wrong answer.
Item types:
- Easy: 21 items; 45 seconds each; 90% accuracy.
- Hard: 9 items; 75 seconds each; 70% accuracy.
Tasks:
- (a) If you attempt all Easy first, then as many Hard as time allows, how many items do you attempt and what is your expected total score?
- (b) Compute expected score per second for Easy vs. Hard and use it to justify the ordering.
- (c) Suppose spending an extra 15 seconds on each Hard raises its accuracy to 78% (so Hard now takes 90s for 78% accuracy). Within the same 1,500s budget and still doing all Easy first, is it optimal to invest the extra time on Hard? Show the optimal mix and expected score, and reconcile your conclusion with the per-second efficiency numbers (note the discrete time constraint).
Solution
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